---
title: "Mo & Bonilla Graphs & Tables"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = F)
knitr::opts_chunk$set(message = F)
knitr::opts_chunk$set(warning = F)
```

```{r}
library(equivtest)
library(haven)
library(stargazer)
library(broom)
library(estimatr)
library(tidyverse)
```


```{r}
## Data Cleaning
s4_dat <- read_csv('s4.csv') %>% 
  filter(
    election_condition == "malestrong" |
      election_condition == "femalestrong" |
      election_condition == "bothstrong"
  ) %>%
  mutate(
    candidate_gender2 = ifelse(candidate_gender == 0, "Male Candidate", "Female Candidate"),
    election_condition2 = case_when(
      election_condition == "bothstrong" ~ "Both\nStrong",
      election_condition == "femalestrong" ~ "Female\nStrong",
      election_condition == "malestrong" ~ "Male\nStrong"
    ),
    f_picked = ifelse(candidate_gender == 1 & choice == 1, 1, 0),
    placement = case_when(order_random == 1 | order_random == 3 | order_random == 5 | order_random == 7 |order_random == 9 | order_random == 11 ~ "Pre", 
                          order_random == 0 | order_random == 2 | order_random == 4 | order_random == 6 | order_random == 8 | order_random == 10 ~ "Post") %>%
      as.factor() %>%
      factor(levels = c("Pre", "Post")),
    symsex = 1-gender_survey
  )
```

## Figure 2

```{r}

s4_dat %>% 
  distinct(subject, .keep_all = T) %>% 
  group_by(placement) %>% 
  summarize(avg_sexism = mean(symsex, na.rm = T), 
            dev_sexism = sd(symsex, na.rm = T), 
            n = n()) %>% 
  mutate(mi = 1.96 * (dev_sexism/sqrt(n)),
         plus = avg_sexism + mi,
         minus = avg_sexism - mi) %>%
  ggplot(aes(x = reorder(placement, desc(placement)), y = avg_sexism, color = placement, shape = placement)) +
  geom_point(size = 2) + 
  geom_errorbar(aes(ymin = minus, ymax = plus), width = .1) + 
  theme_bw() +
  coord_flip() +
  scale_shape_manual(
    name = "Placement of Sensitive Items",
    values = c(1,2),
  ) + 
    scale_color_manual(
    name = "Placement of Sensitive Items",
    values = c("grey65", "grey42"),
  ) +
  labs(x = "", y = "Mean Symbolic Sexism") +
    theme(axis.text=element_text(size=13),
        axis.title=element_text(size=13),
        legend.text=element_text(size=9),
        legend.title=element_text(size=11),
        legend.position = "none",
        legend.key.width = unit(1.5,"cm"),
        legend.spacing.x = unit(0.25,"cm"),
        legend.justification = "center") +
  ylim(0, 1)
```


## Figure 3

```{r}
s4_dat %>% 
  group_by(placement) %>% 
  summarize(avg_score = mean(f_picked, na.rm = T), 
            dev_score = sd(f_picked, na.rm = T), 
            n = n()) %>% 
  mutate(mi = 1.96 * (dev_score/sqrt(n)),
         plus = avg_score + mi,
         minus = avg_score - mi) %>%
  ggplot(aes(x = reorder(placement, desc(placement)), y = avg_score, color = placement, shape = placement)) +
  geom_point(size = 2) + 
  geom_errorbar(aes(ymin = minus, ymax = plus), width = .1) + 
  theme_bw() +
  coord_flip() +
  scale_shape_manual(
    name = "Placement of Sensitive Items",
    values = c(1, 2),
  ) + 
    scale_color_manual(
    name = "Placement of Sensitive Items",
    values = c("grey65", "grey42"),
  ) +
  labs(x = "", y = "Mean Female Candidate Picked") +
    theme(axis.text=element_text(size=13),
        axis.title=element_text(size=13),
        legend.text=element_text(size=9),
        legend.title=element_text(size=11),
        legend.position = "none",
        legend.key.width = unit(1.5,"cm"),
        legend.spacing.x = unit(0.25,"cm"),
        legend.justification = "center") +
  ylim(0, 1)
```


## Figure 4

```{r}
s4_dat %>% 
  group_by(placement, election_condition2) %>% 
  summarize(avg_score = mean(f_picked, na.rm = T), 
            dev_score = sd(f_picked, na.rm = T), 
            n = n()) %>% 
  mutate(mi = 1.96 * (dev_score/sqrt(n)),
         plus = avg_score + mi,
         minus = avg_score - mi) %>%
  ggplot(aes(x = reorder(election_condition2, desc(election_condition2)), y = avg_score, color = reorder(placement, desc(placement)), shape =  reorder(placement, desc(placement)))) +
  geom_point(position = position_dodge(0.3), size = 2) +
  geom_line(position = position_dodge(0.3)) +
  geom_errorbar(aes(ymin = minus, ymax = plus), width = .1, position = position_dodge(0.3)) +
   scale_shape_manual(
    name = "Placement of Sensitive Items",
    values = rev(c(1, 2)),
  ) +  
  scale_color_manual(
    name = "Placement of Sensitive Items",
values = c("grey42", "grey65"),
  ) +
  theme_bw() +
  coord_flip() +
  labs(x = "", y = "Mean Female Candidate Picked")+ 
  theme(axis.text=element_text(size=13),
        axis.title=element_text(size=13),
        legend.text=element_text(size=9),
        legend.title=element_text(size=11),
        legend.position = "bottom",
        legend.box.background = element_rect(colour = "black"),
        legend.key.width = unit(1.5,"cm"),
        legend.spacing.x = unit(0.25,"cm"),
        legend.justification = "center") +
  guides(shape = guide_legend(title.position="top", 
                                    reverse = T), 
               color = guide_legend(title.position="top", 
                                    reverse = T)
        ) +
  ylim(0, 1)
```


## Figure 5

```{r}

  s4_dat %>% 
    mutate(sexism_hl = ifelse(symsex < 0.5, "Low Symbolic Sexism", "High Symbolic Sexism") %>% as.factor() %>% factor(levels = c("Low Symbolic Sexism", "High Symbolic Sexism"))) %>% 
  filter(!is.na(sexism_hl)) %>% 
  group_by(placement, election_condition2, sexism_hl) %>% 
  summarize(avg_score = mean(f_picked, na.rm = T), 
            dev_score = sd(f_picked, na.rm = T), 
            n = n()) %>% 
  mutate(mi = 1.96 * (dev_score/sqrt(n)),
         plus = avg_score + mi,
         minus = avg_score - mi) %>%
  ggplot(aes(x = reorder(election_condition2, desc(election_condition2)), y = avg_score, color =  reorder(placement, desc(placement)), shape =  reorder(placement, desc(placement)))) +
  geom_point(position = position_dodge(0.3), size = 2) +
  geom_line(position = position_dodge(0.3)) +
  geom_errorbar(aes(ymin = minus, ymax = plus), width = .1, position = position_dodge(0.3)) +
   scale_shape_manual(
    name = "Placement of Sensitive Items",
    values = rev(c(1, 2)),
  ) +  
  scale_color_manual(
    name = "Placement of Sensitive Items",
values = c("grey42", "grey65"),
  ) +
  theme_bw() +
  coord_flip() +
  facet_wrap(~sexism_hl) +
  labs(x = "", y = "Mean Female Candidate Picked")+ 
  theme(axis.text=element_text(size=13),
        axis.title=element_text(size=13),
        legend.text=element_text(size=9),
        legend.title=element_text(size=11),
        legend.position = "bottom",
        legend.box.background = element_rect(colour = "black"),
        legend.key.width = unit(1.5,"cm"),
        legend.spacing.x = unit(0.25,"cm"),
        legend.justification = "center", 
        panel.spacing.x = unit(0.75, "lines")) +
  guides(shape = guide_legend(title.position="top", 
                                    reverse = T), 
               color = guide_legend(title.position="top", 
                                    reverse = T)
        ) +
  ylim(0, 1)
```
# Tables - Appendix


## H1 and H2 The Effect of Placement of Symbolic Sexism on the Measurement of Symbolic (H1) and Candidate Evaluation (H2) (Appendix E.5, Table E.36)

```{r}
`studytiming_gender_only` <- s4_dat %>% 
  distinct(subject, .keep_all = T) %>% 
  lm(formula = symsex ~ placement)

`studytiming_candidate_only` <-
  lm(f_picked ~ placement,
     s4_dat)


stargazer(
  `studytiming_gender_only`,
  `studytiming_candidate_only`,
  type = "text",
  covariate.labels = c("Post"),
  dep.var.caption = "Dependent Variable",
  dep.var.labels = c("Symbolic Sexism", "Female Candidate Picked"))
```

## H3: Interaction of Placement of Symbolic Sexism and Treatment on Candidate Evaluation (Appendix E.5, Table E.37)

```{r}
interaction_clusters <-
  lm(
    f_picked ~ as.factor(placement) * election_condition,
    clusters = subject,
    data = s4_dat
  )

stargazer(
  interaction_clusters,
  type = "text",
  dep.var.caption = "Dependent Variable",
  dep.var.labels = "Candidate Score",
  covariate.labels = c(
    "Post",
    "Female Strong",
    "Male Strong",
    "Post x Female Strong",
    "Post x Male Strong",
    "Constant"
   ),
  se = starprep(interaction_clusters),
  star.cutoffs = c(0.05, 0.01, 0.001)
)
```

# H3 T-Tests (Appendix E.5, Table E.38)

```{r}
#different placement across same treatment 
t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "bothstrong"])

t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "femalestrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "femalestrong"])

t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "malestrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "malestrong"])

#different treatment across pre-treatment
t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "femalestrong"])

t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "malestrong"])

t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "malestrong"], s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "femalestrong"])


#different treatment across post-treatment
t.test(s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "femalestrong"])

t.test(s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "malestrong"])

t.test(s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "malestrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "femalestrong"])
```

###  H4: Effect of Placement of Symbolic Sexism x Measurement of Symbolic Sexism x Treatment on Candidate Evaluation (Appendix E.5, Table E.39)

```{r}
interaction_clusters <-
  lm(
    f_picked ~ placement * election_condition  *  symsex,
    clusters = subject,
    data = s4_dat
  )

stargazer(
  interaction_clusters,
  type = "text",
  dep.var.labels = "Candidate Choice",
  se = starprep(interaction_clusters),
  star.cutoffs = c(0.05, 0.01, 0.001)
)
```

## H4: Hi and Low Sym. Sexism (Appendix E.5, Table E.40)

### Low
```{r}
#different placement across same treatment 
data_lss <- s4_dat %>% 
  mutate(symsex_hl = ifelse(symsex < 0.5, "Low Symbolic Sexism", "High Symbolic Sexism")) %>% 
  filter(symsex_hl == "Low Symbolic Sexism")

t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "bothstrong"])

t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "femalestrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "femalestrong"])

t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "malestrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "malestrong"])

#different treatment across pre-treatment
t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "femalestrong"])

t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "malestrong"])

t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "malestrong"], data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "femalestrong"])

#different treatment across post-treatment
t.test(data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "femalestrong"])

t.test(data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "malestrong"])

t.test(data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "malestrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "femalestrong"])
```


### High
```{r}
#different placement across same treatment 
data_hss <- s4_dat %>% 
  mutate(symsex_hl = ifelse(symsex < 0.5, "Low Symbolic Sexism", "High Symbolic Sexism")) %>% 
  filter(symsex_hl == "High Symbolic Sexism")

t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "bothstrong"])

t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "femalestrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "femalestrong"])

t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "malestrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "malestrong"])

#different treatment across pre-treatment
t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "femalestrong"])

t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "malestrong"])

t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "malestrong"], data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "femalestrong"])


#different treatment across post-treatment
t.test(data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "femalestrong"])

t.test(data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "malestrong"])

t.test(data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "malestrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "femalestrong"])
```

# Equiv Tests (Appendix E.7, Table E.41)

```{r}
##pre and post p-value
equiv.t.test(s4_dat$symsex[s4_dat$placement == "Pre"], s4_dat$symsex[s4_dat$placement == "Post"], eps_std = 0.17) %>% summary()

##pre and post p-value
equiv.t.test(s4_dat$f_picked[s4_dat$placement== "Pre"],s4_dat$f_picked[s4_dat$placement== "Post"], eps_std = 0.05) %>% summary()

#different placement across same treatment 
equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "bothstrong"], eps_std = 0.01) %>% summary()

equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "femalestrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "femalestrong"], eps_std = 0.16) %>% summary()

equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "malestrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "malestrong"], eps_std = 0.16) %>% summary()

#different treatment across pre-treatment
equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "femalestrong"], eps_std = 0.37) %>% summary()

equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "malestrong"], eps_std = 0.53) %>% summary()

equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "malestrong"], s4_dat$f_picked[s4_dat$placement == "Pre" & s4_dat$election_condition == "femalestrong"], eps_std = 0.82) %>% summary()

#different treatment across post-treatment
equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "femalestrong"], eps_std = 0.3) %>% summary()

equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "bothstrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "malestrong"], eps_std = 0.46) %>% summary()

equiv.t.test(s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "malestrong"], s4_dat$f_picked[s4_dat$placement == "Post" & s4_dat$election_condition == "femalestrong"], eps_std = 0.67) %>% summary()

## Hi and Low Sym. Sexism
### Low
#different placement across same treatment 
data_lss <- s4_dat %>% 
  mutate(symsex_hl = ifelse(symsex < 0.5, "Low Symbolic Sexism", "High Symbolic Sexism")) %>% 
  filter(symsex_hl == "Low Symbolic Sexism")

equiv.t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "bothstrong"], eps_std = 0.1) %>% summary()

equiv.t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "femalestrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "femalestrong"], eps_std = 0.19) %>% summary()

equiv.t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "malestrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "malestrong"], eps_std = 0.2) %>% summary()

#different treatment across pre-treatment
equiv.t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "femalestrong"], eps_std = 0.37) %>% summary()

equiv.t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "malestrong"], eps_std = 0.6) %>% summary()

equiv.t.test(data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "malestrong"], data_lss$f_picked[data_lss$placement == "Pre" & data_lss$election_condition == "femalestrong"], eps_std = 0.88) %>% summary()

#different treatment across post-treatment
equiv.t.test(data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "femalestrong"], eps_std = 0.3) %>% summary()

equiv.t.test(data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "bothstrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "malestrong"], eps_std = 0.49) %>% summary()

equiv.t.test(data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "malestrong"], data_lss$f_picked[data_lss$placement == "Post" & data_lss$election_condition == "femalestrong"], eps_std = 0.68) %>% summary()

### High
#different placement across same treatment 
data_hss <- s4_dat %>% 
  mutate(symsex_hl = ifelse(symsex < 0.5, "Low Symbolic Sexism", "High Symbolic Sexism")) %>% 
  filter(symsex_hl == "High Symbolic Sexism")

equiv.t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "bothstrong"], eps_std = 0.15) %>% summary()

equiv.t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "femalestrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "femalestrong"], eps_std = 0.15) %>% summary()

equiv.t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "malestrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "malestrong"], eps_std = 0.18) %>% summary()

#different treatment across pre-treatment
equiv.t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "femalestrong"], eps_std = 0.46) %>% summary()

equiv.t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "malestrong"], eps_std = 0.5) %>% summary()

equiv.t.test(data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "malestrong"], data_hss$f_picked[data_hss$placement == "Pre" & data_hss$election_condition == "femalestrong"], eps_std = 0.83) %>% summary()

#different treatment across post-treatment
equiv.t.test(data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "femalestrong"], eps_std = 0.42) %>% summary()

equiv.t.test(data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "bothstrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "malestrong"], eps_std = 0.57) %>% summary()

equiv.t.test(data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "malestrong"], data_hss$f_picked[data_hss$placement == "Post" & data_hss$election_condition == "femalestrong"], eps_std = 0.85) %>% summary()
```



